Foxtrot

At its inception, the Foxtrot was originally danced to ragtime. Today, the dance is customarily accompanied by the same big band music to which swing is also danced.
From the late teens through the 1940s, the Foxtrot was certainly the most popular fast dance and the vast majority of records issued during these years were foxtrots. The waltz and tango, while popular, never overtook the Foxtrot. (Even the popularity of the lindy hop in the 1940s didn't dent the Foxtrot because the Foxtrot could be danced to those lindy hop records, as well.)
When rock and roll first emerged in the early 1950s, record companies were uncertain as to what style of dance would be most applicable to the music. Famously, Decca Records initially labelled its rock and roll releases as "foxtrots", most notably "Rock Around the Clock" by Bill Haley and His Comets. Since that recording, by some estimates, went on to sell more than 25 million copies, "Rock Around the Clock" is technically the biggest-selling "foxtrot" of all time.
Over time, the Foxtrot split into slow (Foxtrot) and quick (Quickstep) versions. In the slow category, further distinctions exist between the International or English style of the Foxtrot and the continuity American style, both built around a slow-quick-quick rhythm at the slowest tempo, and the social American style using a slow-slow-quick-quick rhythm at a somewhat faster pace.
In the context of International Standard category of ballroom dances, for some time Foxtrot was called Slow Foxtrot, or Slowfox. These names are still in use, to distinguish from other types of Foxtrot.